Phase-based direct average strain estimation for elastography

In this paper, a phase-based direct average strain estimation method is developed. A mathematical model is presented to calculate axial strain directly from the phase of the zero-lag cross-correlation function between the windowed precompression and stretched post-compression analytic signals. Unlike phase-based conventional strain estimators, for which strain is computed from the displacement field, strain in this paper is computed in one step using the secant algorithm by exploiting the direct phase-strain relationship. To maintain strain continuity, instead of using the instantaneous phase of the interrogative window alone, an average phase function is defined using the phases of the neighboring windows with the assumption that the strain is essentially similar in a close physical proximity to the interrogative window. This method accounts for the effect of lateral shift but without requiring a prior estimate of the applied strain. Moreover, the strain can be computed both in the compression and relaxation phases of the applied pressure. The performance of the proposed strain estimator is analyzed in terms of the quality metrics elastographic signal-to-noise ratio (SNRe), elastographic contrast-to-noise ratio (CNRe), and mean structural similarity (MSSIM), using a finite element modeling simulation phantom. The results reveal that the proposed method performs satisfactorily in terms of all the three indices for up to 2.5% applied strain. Comparative results using simulation and experimental phantom data, and in vivo breast data of benign and malignant masses also demonstrate that the strain image quality of our method is better than the other reported techniques.